Follow Up: For one of the bones discussed above, graph the equations for males and females on the same set of axes. What do the x- and y-intercepts represent in terms of this problem? Does this make sense? Why?
Tibia
x-axis: Length of the Tibia y-axis: Height female x-intercept: -34.15 This is where the line crosses the x-axis. This shows the length of the tibia when the height is at 0 (according to the equation.) male x-intercept: -28.65 This is where the line crosses the x-axisThis shows the length of the tibia when the height is at 0 (according to the equation.) female y-intercept: 72.572 This is where the line crosses the y-axisThis shows the height when the length of the tibia is at 0 (according to the equation.) male y-intercept: 81.688 This is where the line crosses the y-axisThis shows the length of the height when the length of the tibia is at 0 (according to the equation.)
Noel Oracheski
Math 7B
4.3 Analyzing Bones
Answer the following questions according to this table.
A. How tall is a female if her femur is 46.2 centimeters long?
This is the equation to find the height of a female from the length of her femur: h = 61.412 + 2.317F
F = Length of Femur = 46.2
h = 61.412 + 2.317 x 46.2 = 168.4574
HEIGHT = 168.4574
B. How tall is a male if his tibia is 50.1 centimeters long?
This is the equation to find the height of a male from the length of his tibia: h = 81.688 + 2.392T
T = Length of Tibia = 50.1
h
81.688 + 2.392 x 50.1
201.5272HEIGHT = 201.5272
C. If a woman is 152 centimeters (about 5 feet) tall, how long is her femur? Her tibia? Her humerus? Her radius?
Femur: 39.09710833 cm
Tibia: 31.35728385
Hemurus: 27.67907125
Radius: 20.24972
Femur:
-61.1412 + 152 = 61.1412 + 2.317x - 61.1412
90.588 / 2.317 = 2.317x / 2.317
39.09710833 = x
Tibia:
-72.572 + 152 = 72.572 + 2.533x -72.572
79.428 / 2.533 = 2.533x / 2.533
31.35728385 = x
Hemurus:
-64.977 + 152 = 64.977 + 3.144x -64.977
87.023 / 3.144 = 3.144x / 3.144
27.67907125 = x
Radius:
-73.502 + 152 = 73.502 + 3.876x -73.502
78.498 / 3.876 = 3.144x / 3.876
20.249742 = x
D. If a man is 183 centimeters (about 6 feet) tall, how long is his femur? His tibia? His humerus? His radius?
Femur: 50.89857015
Tibia: 42.3545151
Hemurus: 36.8451178
Radius: 28.1082192
Femur:
-69.089 + 183 = 69.089 + 2.238x -69.089
113.911 / 2.238 = 2.238x / 2.238
50.89857015 = x
Tibia:
-81.688 + 183 = 81.688 + 2.392x -81.688
101.312 / 2.392 = 2.392x / 2.392
42.3545151 = x
Hemurus:
-73.570 + 183 = 73.570 + 2.970x -73.570
109.43 / 2.970 = 2.970x/ 2.970
36.8451178= x
Radius:
-80.405 + 183 = 80.405 + 3.650x -80.405
102.595 / 3.650 = 3.650x / 3.650
28.1082192 = x
Follow Up:
For one of the bones discussed above, graph the equations for males and females on the same set of axes. What do the x- and y-intercepts represent in terms of this problem? Does this make sense? Why?
Tibia
x-axis: Length of the Tibia
y-axis: Height
female x-intercept: -34.15 This is where the line crosses the x-axis. This shows the length of the tibia when the height is at 0 (according to the equation.)
male x-intercept: -28.65 This is where the line crosses the x-axis This shows the length of the tibia when the height is at 0 (according to the equation.)
female y-intercept: 72.572 This is where the line crosses the y-axis This shows the height when the length of the tibia is at 0 (according to the equation.)
male y-intercept: 81.688 This is where the line crosses the y-axis This shows the length of the height when the length of the tibia is at 0 (according to the equation.)